Blog · Finance metrics and formulas · Supply chain
Ordering cost rises with order frequency, while carrying cost rises with average inventory. Compare annual order-size scenarios using the same demand, cost definitions, and service assumptions.
Ordering cost and carrying cost move in opposite directions when you change replenishment quantity under otherwise stable conditions. Larger orders mean fewer purchasing transactions but more inventory waiting to be used. Compare both on an annual basis, then test whether the resulting quantity fits actual supplier and service constraints.
Ordering cost covers the work triggered by an order: preparation, approval, supplier communication, receiving administration, and invoice processing within your defined scope. It is expressed as dollars per order before being multiplied by order frequency.
Carrying cost covers inventory held over time. Use an annual cost per unit or an annual percentage of inventory cost, with the components defined consistently. The separate carrying cost calculation covers capital, storage, service, and risk components in detail.
| Question | Ordering cost | Carrying cost |
|---|---|---|
| What drives it in the simple comparison? | Number of orders | Average inventory |
| Input unit | USD per order | USD per unit per year |
| Annual calculation | Orders × Cost per order | Average units × Annual holding cost per unit |
| Effect of a larger order quantity | Usually decreases | Usually increases |
| Main evidence | Purchasing and receiving activity | Inventory valuations and holding expense pools |
Use activity-based costing when the transaction cost needs to be built from labor and shared expense pools. An allocated cost per order describes resource consumption; it does not guarantee the same cash saving when one order is removed.
Use the item demand history to establish annual units, excluding warehouse transfers that do not represent consumption. Use purchase order headers to count orders at the level that triggers the stated transaction cost. Use receipt and inventory records to understand actual delivery patterns.
For the worked comparison, a US distributor buys one item at a constant unit cost. The following are illustrative planning inputs, not market benchmarks.
| Input | Symbol | Value | Basis |
|---|---|---|---|
| Annual demand, units | D | 12,000 | Item consumption for the year |
| Cost per order (USD) | S | 75 | Assigned ordering activity cost |
| Unit inventory cost (USD) | C | 25 | Consistent acquisition cost basis |
| Annual carrying rate | i | 20.0% | Stated management assumption |
| Annual carrying cost per unit (USD) | H | 5 | 25 × 20.0% |
The acquisition cost basis matters even though purchase spending is constant in this example. IRS Publication 538 describes purchased merchandise cost as invoice price after appropriate discounts plus transportation and other acquisition charges. Use a consistent valuation basis when turning a percentage into an annual holding cost per unit.
Assume constant demand, immediate full receipts, no shortages, no quantity discounts, and no safety stock for the initial comparison. Inventory falls evenly from the order quantity to zero, so its average is half the order quantity.
Annual ordering cost = (D / Q) × S
Annual carrying cost = (Q / 2) × H
Combined annual relevant cost = (D / Q) × S + (Q / 2) × H
Here Q is the order quantity in units. These equations describe the stated scenario; uneven demand and staggered receipts need observed inventory averages instead.
| Order quantity, units | Annual orders: D / Q | Average cycle inventory: Q / 2 | Ordering cost (USD) | Carrying cost (USD) | Combined cost (USD) |
|---|---|---|---|---|---|
| 300 | 40 | 150 | 3,000 | 750 | 3,750 |
| 600 | 20 | 300 | 1,500 | 1,500 | 3,000 |
| 1,200 | 10 | 600 | 750 | 3,000 | 3,750 |
For orders of 600 units, 12,000 / 600 = 20 orders. Ordering expense is 20 × $75 = $1,500. Average cycle inventory is 600 / 2 = 300 units, carrying cost is 300 × $5 = $1,500, and combined cost is $3,000.
Buying 300 units each time adds $750 to the combined annual cost relative to buying 600. Buying 1,200 also adds $750, but the source is excess carrying cost rather than ordering activity. Annual purchase spending is unchanged at 12,000 × $25 = $300,000 in all three scenarios.
Place D, S, and H in B1:B3. Put the candidate Q in A6. Enter these Excel formulas in B6:F6, respectively, then fill down for other candidates:
=$B$1/A6
=A6/2
=B6*$B$2
=C6*$B$3
=D6+E6
Check that =B6*A6 returns annual demand for every row. Also check that annual cost uses a per-year holding input, rather than a monthly amount left unconverted.
For an independent total, put the scenario's annual orders and average units in H6:H7, with their respective rates S and H in I6:I7:
=SUMPRODUCT(H6:H7,I6:I7)
For the 600-unit scenario this calculates 20 × 75 + 300 × 5 = $3,000. Microsoft's SUMPRODUCT documentation confirms that the function sums products of matching arrays. Covirage is not affiliated with Microsoft.
Under these assumptions, balancing the two cost terms gives Q = √(2DS/H). Substituting the stated inputs gives √(2 × 12,000 × 75 / 5) = 600 units. The three-scenario table supports that result without implying that actual purchasing can ignore constraints.
Suppose every scenario also needs the same 100 units of safety stock. The extra annual carrying cost is 100 × $5 = $500. Combined costs become $4,250, $3,500, and $4,250 in table order. The ranking stays the same because the same amount was added to each scenario.
If order size changes delivery reliability or the required buffer, hold neither of those constant without evidence. Review supplier lead times, storage limits, and expiration dates with procurement and warehouse owners. The relationship between customer delivery frequency and cost is addressed separately in order size and drop frequency.
Bring a file of demand, purchasing activity, inventory values, and your stated scenario assumptions; Covirage maps the columns, and its tools compute and check the cost comparisons. The external AI model explains the results with every figure traced to its rows. Create a free Covirage account and bring a sample of your own data; creating the account takes about a minute.
See Covirage for supply chain teams for the supporting context.
The unit purchase price is usually separate from the administrative cost per order. If the unit price stays constant across scenarios, annual purchase spending stays constant too. Include price breaks, freight differences, or other changing purchase costs separately when they affect the decision.
Under steady demand and immediate replenishment, cycle inventory declines from the receipt quantity to zero before the next delivery. A larger receipt therefore raises average cycle inventory. Safety stock and other inventory buffers must be added separately using consistent service assumptions.
It is a starting point under the stated assumptions. Supplier minimums, pack sizes, shelf life, capacity, uncertain demand, and required service levels may rule it out. Compare feasible quantities and document those constraints before changing purchasing instructions.